Question

Tn=3, Sn=144 and n=9 find a.

Answer 1

HEY THERE!!!


Question;

Tn=3, Sn=144 and n=9 find a.

Given;

Number of terms = 3

Total Number of sum = 144

Number = 9



To find ; First term (a) =?



Method Of Solution!

Using Summation Formula!!

Summation Formula: Sn= n/2(a+l)

Substitute the Given value in Summation Formula!!

=> Sn = n/2(a+l)

=> 144= 9/2(a+3)

=> 144 × 2 = 9(a+3)

=> 288 = 9a+27

=> 288-27 = 9a

=>261 =9a

•°• a= 261/9

=> 29

Hence, First Term (a) = 29

Answer 2

In an A.P,

Let the first term be a

Let the common difference be d

Tn is the value of the nth term.

We know that:

Tn=a+(n-1)d

Given:

Tn=3

So:-

a+(n-1)d=3.....................................(1)

Now we also know that:

Sn is the sum of all terms from a till n.

Sn=n/2*[2a+(n-1)d]

Given,

Sn=144

We know that :-

2a+(n-1)d

==>a+a+(n-1)d

==>a+3 [ From (1) ]

So:

144=n/2*[a+3]

but n is 9

==>144*2=9[a+3]

==>a+3=288/9

==>a+3=32

==>a=32-3

==>a=29

The value of a is 29.

Enjoy maths hope it was helpful:-)

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